Publications

(see also my page on Google Scholar)

Preprints (Submitted)



Journals

  1. G. Katsiolides, E.H. Müller, R. Scheichl, T. Shardlow, M.B. Giles and D.J. Thomson (2018), Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling, Journal of Computational Physics 354:320-343 [Preprint]

  2. A. Reinarz, T. Dodwell, T. Fletcher, L. Seelinger, R. Butler and R. Scheichl (2018), dune-composites - A New Framework for High-Performance Finite Element Modelling of Laminates, Composite Structures 184:269-278 [Preprint]

  3. D Drzisga, B. Gmeiner, U. Rüde, R. Scheichl and B. Wohlmuth (2017), Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods, SIAM Journal on Scientific Computing 39(5):S873-S897 [Preprint]

  4. F.Y. Kuo, R. Scheichl, Ch. Schwab, I.H. Sloan and E. Ullmann (2017), Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems, Mathematics of Computation 86:2827-2860 [Preprint]

  5. R. Scheichl, A. Stuart and A.L. Teckentrup (2017), Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems, SIAM/ASA Journal on Uncertainty Quantification 5(1):493-518. [Preprint]

  6. D. Peterseim and R. Scheichl (2016), Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast, Computational Methods in Applied Mathematics 16(4):579-603. [Preprint]

  7. T.A. Fletcher, T. Kim, T.J. Dodwell, R. Butler, R. Scheichl and R. Newley (2016), Resin Treatment of Free Edges to Aid Certification of Through Thickness Laminate Strength, Composite Structures 146:26-33.

  8. A. Ferreiro-Castilla, A.E. Kyprianou and R. Scheichl (2016), An Euler-Poisson Scheme for Levy driven SDEs, Journal of Applied Probability 53(1):262-278. [Preprint (Sept 2013)]

  9. A. Dedner, E.H. Mueller and R. Scheichl (2016), Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio, International Journal for Numerical Methods in Fluids 80(1):76-102 [Preprint]

  10. I.G. Graham, R. Scheichl and E. Ullmann (2015), Mixed Finite Element Analysis of Lognormal Diffusion and Multilevel Monte Carlo Methods, Stochastics and Partial Differential Equations: Analysis and Computations 4(1):41-75, [Preprint (Dec 2013)]

  11. S. Loisel, H. Nguyen and R. Scheichl (2015), Optimized Schwarz and 2-Lagrange Methods for Multiscale PDEs, SIAM Journal of Scientific Computing 37(6):A2896–A2923 [Preprint]

  12. E.H. Mueller, R. Scheichl and E. Vainikko (2015), Petascale Solvers for Anisotropic PDEs in atmospheric modelling on GPU Clusters, Parallel Computing 50:53-69 [Preprint]

  13. T.J. Dodwell, C. Ketelsen, R. Scheichl and A.L. Teckentrup (2015), A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow, SIAM/ASA Journal on Uncertainty Quantification 3(1):1075-1108 [Preprint (v1: Mar 2013)]

  14. E.H. Mueller, R. Scheichl and T. Shardlow (2015), Improving MLMC for SDEs with Application to the Langevin Equation, Proceedings of the Royal Society A 471:20140679 [Preprint]

  15. I.G. Graham, F.Y. Kuo, J.A. Nicholls, R. Scheichl, Ch. Schwab and I.H. Sloan (2015), Quasi-Monte Carlo Finite Element Methods for Elliptic PDEs with Log-normal Random Coefficients, Numerische Mathematik 131(2):329-368 [Preprint (May 2013)]

  16. M. Dauge, R.A. Norton and R. Scheichl (2014), Regularity of Maxwell Eigenproblems in Photonic Crystal Fibre Modelling, BIT Numerical Mathematics 55(1):59-80 [Preprint]

  17. E.H. Mueller and R. Scheichl (2014), Massively Parallel Solvers for Elliptic PDEs in Numerical Weather- and Climate Prediction, Quarterly J Royal Meteorological Society 140(685):2608-2624 [Preprint]

  18. A. Ferreiro-Castilla, A.E. Kyprianou, R. Scheichl and G. Suryanarayana (2014), Multilevel Monte Carlo Simulation for Levy Processes Based on the Wiener-Hopf Factorisation, Stochastic Processes and their Applications 124(2):985-1010 [Preprint (Oct 2012)]

  19. N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl (2014), Abstract Robust Coarse Spaces for Systems of PDEs via Generalized Eigenproblems in the Overlaps , Numerische Mathematik 126(4):741-770 [Preprint (Nov 2011)]

  20. E. Mueller, X. Guo, R. Scheichl and S. Shi (2013), Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs, Computing and Visualization in Science 16(2):41-58 [Preprint]

  21. A.L. Teckentrup, R. Scheichl, M.B. Giles and E. Ullmann (2013), Further Analysis of Multilevel Monte Carlo Methods for Elliptic PDEs with Random Coefficients, Numerische Mathematik 125(3):569-600 [Preprint]

  22. J. Charrier, R. Scheichl and A.L. Teckentrup (2013), Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and its Application to Multilevel Monte Carlo Methods, SIAM Journal on Numerical Analysis 51 (1):322-352 [Preprint (April 2011)]

  23. R. Norton and R. Scheichl (2012), Planewave Expansion Methods for Photonic Crystal Fibres, Applied Numerical Mathematics 63:88-104 [Preprint]

  24. C. Pechstein and R. Scheichl (2012), Weighted Poincare Inequalities, IMA Journal on Numerical Analysis 33 (2):652--686 [Preprint (Dec 2010)]

  25. V. Dolean, F. Nataf, R. Scheichl and N. Spillane (2012), Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps, Computational Methods in Applied Mathematics 12 (4):391-414, [Preprint]

  26. R. Scheichl, P.S. Vassilevski and L.T. Zikatanov (2012), Mutilevel Methods for Elliptic Problems with Highly Varying Coefficients on Non-Aligned Coarse Grids, SIAM Journal on Numerical Analysis 50 (3):1675-1694 [Preprint (Aug 2010)]

  27. M. Marletta and R. Scheichl (2012), Eigenvalues in Spectral Gaps of Differential Operators, Journal of Spectral Theory 2 (3):293-320 [Preprint (Sept 2010)]

  28. P. Bastian, M. Blatt and R. Scheichl (2012), Algebraic Multigrid for Discontinuous Galerkin Discretizations, Numerical Linear Algebra with Applications 19 (2):367-388 [Preprint]

  29. N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl (2011), A Robust Two Level Domain Decomposition Preconditioner for Systems of PDEs, Comptes Rendus Mathematique 349 (23-24):1255-1259 [Preprint]

  30. R. Scheichl, P.S. Vassilevski and L.T. Zikatanov (2011), Weak Approximation Properties of Elliptic Projections with Functional Constraints, Multiscale Modeling and Simulation and Analysis 9 (4):1677-1699 [Preprint]

  31. K.A. Cliffe, M.B. Giles, R. Scheichl and A.L. Teckentrup (2011), Multilevel Monte Carlo Methods and Applications to Elliptic PDEs with Random Coefficients, Computing and Visualization in Science 14 (1):3-15 [Preprint]

  32. S.D. Buckeridge, M.J.P. Cullen, R. Scheichl and M. Wlasak (2011), A Robust Numerical Method for the Potential Vorticity Based Control Variable Transform in Variational Data Assimilation, Quarterly J Royal Meteorological Soc 137 (657):1083-1094

  33. C. Pechstein and R. Scheichl (2011), Analysis of FETI Methods for Multiscale PDEs - Part II: Interface Variation, Numerische Mathematik 118 (3):485-529 [Preprint (July 2009)]

  34. I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan (2011), Quasi-Monte Carlo Methods for for Elliptic PDEs with Random Coefficients and Applications, Journal of Computational Physics 230 (10):3668-3694 [Preprint]

  35. S.D. Buckeridge and R. Scheichl (2010), Parallel Geometric Multigrid for Global Weather Prediction, Numerical Linear Algebra with Applications 17:325-342 [Preprint]

  36. R. Norton and R. Scheichl (2010), Convergence Analysis of Planewave Expansion Methods for Schroedinger Operators with Discontinuous Periodic Potentials, SIAM Journal for Numerical Analysis 47 (6):4356-4380 [Preprint]

  37. C. Pechstein and R. Scheichl (2009), Scaling Up through Domain Decomposition, Applicable Analysis 88(10):1589-1608 [Preprint]

  38. J. Van lent, R. Scheichl and I.G. Graham (2009), Energy Minimizing Coarse Spaces for Two-level Schwarz Methods for Multiscale PDEs, Numerical Linear Algebra with Applications 16(10):775-799 [Preprint]

  39. C. Pechstein and R. Scheichl (2008), Analysis of FETI Methods for Multiscale PDEs, Numerische Mathematik 111(2):293-333 [Preprint]

  40. B. Aksoylu, I.G. Graham, H. Klie and R. Scheichl (2008), Towards a Rigorously Justified Algebraic Preconditioner for High-Contrast Diffusion Problems, Computing and Visualization in Science 11, pp. 319-331 [Preprint]

  41. R. Scheichl and E. Vainikko (2007), Additive Schwarz with Aggregation-Based Coarsening for Elliptic Problems with Highly Variable Coefficients, Computing 80(4):319-343 [Preprint]

  42. I.G. Graham, P. Lechner and R. Scheichl (2007), Domain Decomposition for Multiscale PDEs, Numerische Mathematik 106:589-626 [Preprint]

  43. I.G. Graham and R. Scheichl (2007), Robust Domain Decomposition Algorithms for Multiscale PDEs, Numerical Methods for Partial Differential Equations 23(4):859-878 [Preprint]

  44. R. Scheichl, M.-H. Klopffer, Z. Benjelloun-Dabaghi, B. Flaconneche (2005), Permeation of Gases in Polymers: Parameter Identification and Nonlinear Regression Analysis, Journal of Membrane Science 254, pp. 275-293 [PostScript file]

  45. R. Scheichl, R. Masson, J. Wendebourg (2003), Decoupling and Block Preconditioning for Sedimentary Basin Simulations, Computational Geosciences 7(4), pp. 295-318 [Abstract ] [Preprint]

  46. R. Scheichl (2002), Decoupling Three-dimensional Mixed Problems Using Divergence-free Finite Elements. (SIAM Student Paper Prize 2000) SIAM Journal of Scientific Computing 23 (5):1752-1776 [Abstract ] [Preprint]

  47. K.A. Cliffe, I.G. Graham, R. Scheichl, and L. Stals (2000), Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements. Journal of Computational Physics 164:258-282 [Abstract] [Preprint]

  48. R. Scheichl (2000), Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations. International Journal for Numerical Methods in Engineering 47:1751-1771 [Abstract] [Preprint]


Books

  1. M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors) (2013), Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences, Radon Series on Computational and Applied Mathematics, Vol. 13, De Gruyter, Berlin [De Gruyter Link]

  2. P. Bastian, J. Kraus, R. Scheichl and M.F. Wheeler (Editors) (2013), Simulation of Flow in Porous Media: Applications in Energy and Environment, Radon Series on Computational and Applied Mathematics, Vol. 12, De Gruyter, Berlin [De Gruyter Link]

  3. I.G. Graham, T.Y. Hou, O. Lakkis and R. Scheichl (Editors) (2012), Numerical Analysis of Multiscale Problems, Lecture Notes in Computational Science and Engineering, Vol. 83, Springer, Heidelberg [Springer Link]

  4. R. Scheichl (1997), Parallel Solution of the Transient Multigroup Neutron Diffusion Equations with Multi-Grid and Preconditioned Krylov-Subspace Methods (Master's Thesis). Schriften der Johannes Kepler Universitaet Linz, Vol. C21 , Trauner-Verlag, Linz [PostScript file (without large colour picture)]


Refereed Proceedings

  1. I.G. Graham, M.J. Parkinson and R. Scheichl (2018), Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport, invited article for the "Festschrift for the 80th birthday of Ian Sloan" (Dick J, Kuo FY, Wozniakowski H, Eds.), Springer [Preprint]

  2. T.J. Dodwell, A. Sandhu and R. Scheichl (2017), Customized Coarse Models for Highly Heterogeneous Materials, in "Bifurcation and Degradation of Geomaterials with Engineering Applications" (Papamichos E, Papanastasiou P, Pasternak E, Dyskin A, Eds.), IWBDG 2017, Springer Series in Geomechanics and Geoengineering, Springer [Preprint]

  3. T. Fletcher, A. Reinarz, T.J. Dodwell, R. Butler, R. Scheichl and R. Newley (2016), Efficient Modelling and Accurate Certification of Curved Aerospace Laminates, 17th European Conference on Composite Materials, Munich, 26-30 June 2016 [Link]

  4. R. Butler, T.J. Dodwell, T. Kim, S. Kynaston, R. Scheichl, R.T. Haftka and N.H. Kim (2015), Uncertainty Quantification of Composite Structures with Defects using Multilevel Monte Carlo Simulations, AIAA SciTech Conference, Kissimmee, 5-9 January 2015 [Link]

  5. T. Kim, T. Fletcher, T.J. Dodwell, R. Butler, R. Scheichl, J. Ankersen and R. Newley (2015), The Effect of Free Edges on Inter-Laminar Performance of Curved Laminates, AIAA SciTech Conference, Kissimmee, 5-9 January 2015 [Link]

  6. R. Scheichl (2014), Robust Numerical Upscaling at High Contrast, Oberwolfach Workshop on "Reactive Flows in Deformable, Complex Media" (Organisers: M.~Gerritsen, J.M.~Nordbotten, I.S.~Pop, B.~Wohlmuth), 21-27 September 2014, Oberwolfach Report 43/2014 [PDF]

  7. N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R Scheichl (2014), Achieving Robustness Through Coarse Space Enrichment in the Two Level Schwarz Framework, to appear in Proceedings of the 21st International Conference on Domain Decomposition Methods (DD21), Rennes, June 2012 [Preprint]

  8. R. Scheichl (2013), MLMCMC -- Multilevel Markov Chain Monte Carlo, Oberwolfach Miniworkshop on "Numerical Upscaling for Media with Deterministic and Stochastic Heterogeneity" (Organisers: Y. Efendiev, O. Iliev, P. Vassilevski), 10-16 February 2013, Oberwolfach Report 07/2013 [PDF]

  9. R. Scheichl (2013), Robust Coarsening in Multiscale PDEs, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 51-62. [Preprint]

  10. C. Pechstein, M. Sarkis and R. Scheichl (2013), New Theoretical Coefficient Robustness Results for FETI-DP, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 313-320. [Preprint]

  11. V. Dolean, F. Nataf, R. Scheichl and N Spillane (2013), A Two-Level Schwarz Preconditioner for Heterogeneous Problems, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 87-94. [Preprint]

  12. C. Pechstein and R. Scheichl (2011), Weighted Poincare Inequalities and Applications in Domain Decomposition, Domain Decomposition Methods in Science and Engineering XIX (Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, eds.), Lecture Notes in Computational Science and Engineering, vol. 78, pp. 197-204 (Proceedings of 19th Int. Conf. Domain Decomposition Methods, 17-22 Aug 2009, Zhangjiajie, China). [Preprint]

  13. E. Dodgson, D.A.S. Rees and R. Scheichl (2010), Vortex Instability of Free Convection Boundary Layers in Porous Media, in Proceedings of 3rd Internat. Conf. Porous Media and its Applications in Science, Engineering and Industry, June 20-25 2010, Montecatini, Italy, AIP Conference Proceedings, Vol. 1254, K. Vafai (Ed.)

  14. C. Pechstein and R. Scheichl (2010), Robust FETI Solvers for Multiscale Elliptic PDEs, in Proceedings of the 6th Int. Conf. on Scientific Computing in Electrical Engineering (SCEE 2008, Helsinki, Sep 2008), Roos, J., Costa, L.R.J. (Eds.), volume 14 of Mathematics in Industry, Springer, pp. 421-428 [Preprint]

  15. C. Pechstein and R. Scheichl (2010), Weighted Poincare Inequalities for High-Contrast Coefficients, Oberwolfach Workshop on "Computational Electromagnetism and Accoustics" (Organisers: R Hiptmair, RHW Hoppe, P Joly, U Langer), 14-20 February 2010, Oberwolfach Report 10/2010 [PDF] [Full Report]

  16. R. Scheichl (2009), Domain Decomposition and Upscaling, Oberwolfach Miniworkshop on "Numerical Upscaling for Flow Problems: Theory and Applications" (Organisers: A. Brandt, Y. Efendiev, O. Iliev), 1-7 March 2009, Oberwolfach Report 12/2009 [PDF] [Full Report]

  17. I.G. Graham and R. Scheichl (2008), Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz, in Proceedings of the 17th International Conference on Domain Decomposition Methods, Strobl, Austria, 3-7 July 2006, Langer, U., Discacciati, M. Keyes, D. et al. (Eds.), Domain Decomposition Methods in Science and Engineering XVII, Lecture Notes in Computational Science and Engineering, Vol. 60, Springer, New York [Preprint]

  18. R. Scheichl and E. Vainikko (2006), Robust Aggregation-Based Coarsening for Additive Schwarz in the Case of Highly Variable Coefficients, in Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006 (P. Wesseling, E. Onate, J. Periaux, Eds.), TU Delft [Preprint]

  19. R. Masson, P. Quandalle, S. Requena, R. Scheichl (2004), Parallel Preconditioning for Sedimentary Basin Simulations, Lecture Notes in Computer Science 2907 (Lirkov I., Margenov S. et al., Eds.), Proceedings 4th Int. Conf. on Large Scale Scientific Computations, June 4-8, 2003, Sozopol, Bulgaria, Springer [Abstract ] [PostScript file]

  20. R. Scheichl (1999), Parallel Solvers for the Two-Group Neutron Diffusion Equations of Reactor Kinetics. Proceedings of the 11th International Conference on Domain Decomposition Methods, Greenwich, July 1998 (edited by C.H. Lai et al.) [PostScript file]

  21. H. Finnemann and R. Scheichl (1999), Efficiency Enhancements of Coupled RELAP5/PANBOX Calculations Using Adaptive Methods. Transactions of the American Nuclear Society for the Annual Meeting, Boston, June 1999 [WordDocument]


Theses



Extended Abstracts and Other Publications


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Last updated 20/12/2013